First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
PLANAR ALGEBRIC CURVES
SCM0014408, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
N0
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination PLANAR ALGEBRIC CURVES
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge ALESSANDRA BERTAPELLE MAT/03

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/03 Geometry 7.0

Mode of delivery (when and how)
Period First semester
Year 3rd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
6 Curve Algebriche Piane - 2017/2018 01/10/2017 30/09/2018 BERTAPELLE ALESSANDRA (Presidente)
FIOROT LUISA (Membro Effettivo)
CAILOTTO MAURIZIO (Supplente)
CANDILERA MAURIZIO (Supplente)
KLOOSTERMAN REMKE NANNE (Supplente)
NOVELLI CARLA (Supplente)

Syllabus
Prerequisites: Prerequisites: algebra and geometry courses of the first and second year.
Target skills and knowledge: The aim of the course is to introduce students to the study of fundamental (elementary) algebraic curves in the affine and projective plane:
singular points, tangents, intersection, local analysis; classification of cubics and group law on elliptic curves.
Examination methods: The final examination consists of two parts, a written one and an oral one. The written test can be splitted in two partial tests ("compitini").
Assessment criteria: The written part is devoted to the study of the elementary aspects of a plane algebraic curve and to solving simple problems on theoretical topics of the course. The oral exam is intedended to evaluate theoretical skills acquired during the course and the ability to apply them.
Course unit contents: After recalling affine and projective spaces, we will study geometric properties of affine and projective curves by introducing algebraic tools that serve the purpose. These are the principal topics:
singular points and their tangent complexes, rational curves, polar curves; inflection points, Hessian curves (algebraic tool: algebraic differential calculus for polynomials).
Classification and geometry of the cubics; elliptic curves.
Intersection of plane curves, Bezout's theorem (algebraic tools: the resultant of two polynomials and the discriminant).
Local study of curves: branches, places, centers (algebraic tools: formal power series and Puiseux series).
Planned learning activities and teaching methods: Lectures on a chalkboard. Possible use of a tablet.
Additional notes about suggested reading: The course is based on the course notes "Curve Algebriche Piane" by Maurizio Cailotto.
Exercises of the past exams are collected in a e-book. Both sources will be available at the e-learning page.
Textbooks (and optional supplementary readings)